A fuzzy goal programming model with probabilistic constraints based on the poisson distribution - Khairiyah Manurung, Silvi; Mardiningsih; Saib Suwilo (Universitas Islam Negeri Raden Intan Lampung, 2025)
Uncertainty and fuzzy ambiguity often complicate multi-objective decision-making, especially when discrete random events influence system behavior, making classical deterministic models insufficient. This study aims to develop a Probabilistic Fuzzy Goal Programming (PFGP) model that incorporates the Poisson distribution by reformulating the right-hand side (RHS) constraints into probabilistic expressions to more accurately represent discrete uncertainty. The methodological approach includes revisiting PFGP theory, defining decision variables and fuzzy aspiration levels, constructing probabilistic constraints, and applying the Poisson distribution to characterize randomness in constraint parameters, with the probabilistic constraints subsequently transformed into deterministic equivalents using the Poisson quantile function to ensure computational tractability. The results demonstrate that the proposed Poisson-based PFGP model produces more realistic, flexible, and robust decision alternatives in dynamic environments involving event-count data. The study contributes a Poisson-driven quantile reformulation mechanism for RHS constraints, offering a novel and effective pathway for handling discrete uncertainty within multi-objective fuzzy optimization.